EXPERIMENTAL SCIENCES. Time allowed, 2 hours. [N.B.-Not more than 10 of the following questions are to be answered.] 1. Describe the construction and explain the action of a minimum thermometer. Explain why such an instrument, if freely exposed to the sky, will not give accurately the minimum temperature of the air. 2. State the law of expansion of air for changes of temperature. A certain weight of air occupies 5.6 cubic inches at 21° C.; how much will it occupy at 99° under the same pressure? 3. Give the observed laws of fusion and solidification by heat or cold, and explain how to make an experiment in confirmation of the truth of these laws in the case of tin. What is meant when it is said that the latent heat of tin is 14.25? 4. What is the relation between the radiating and absorbing powers for heat of the same surfaces? Give some experiment in illustration of the truth of your statement. Considering this relation between absorbing and radiating powers, how does it come to pass that different bodies placed in sunshine acquire different temperatures? 5. Describe one form of hygrometer, and explain its action. 6. Give an account of the different modifications of sulphur, and how they are severally obtained. How much sulphuretted hydrogen and sulphuric acid, respectively, can be obtained from 54 4 grains of sulphur? (S= 32.) 7. Describe a method of preparing and collecting chlorine, and explain the chemistry of the process. Explain the action of chlorine on sulphuretted hydrogen. 8. State the chemical composition of marble, coal, rust of iron, alum. How can you distinguish potash alum from ammonia alum? Name the 9. What are the chief chemical characters of an alkali? alkalies. How can soda be obtained from the carbonate? 10. Explain the blackening of a china plate when it is held in the flame of a gas lamp. Also why the brilliancy of an oil lamp is increased by the use of a glass chimney. 11. Give blowpipe tests for manganese and magnesia, and liquid tests for zinc sulphate, explaining how to apply the tests and the results of them. 12. State the laws of induction in static electricity, and give some experimental illustrations of them. Show that the fact that the two coatings of a Leyden jar are usually unequally charged is in accordance with those laws. 13. An iron bar, supported on a gutta-percha stand, has pairs of pith balls hung from it by cotton at different points; state how the balls will behave when the bar is electrified. Explain how they will be affected if you approach your hand to one end of the bar without drawing a spark. 14. Describe the construction of a galvanometer, and the mode of using it. If you want to make one-hundredth part of the current from a battery, and no more, pass through your galvanometer, explain how you would effect this. 15. A silver and a copper plate are soldered together and immersed in a solution of copper sulphate; state and explain the result. After a time all action will cease; explain when that will happen. 16. You want to make a powerful permanent magnet; what would you choose to make it of, and how would you proceed to make it, supposing you were not provided with any other magnet? Which end of the magnet so made would point to the north if the magnet were hung up by a thread? 17. Define the declination of a compass. What is, roughly, the amount of the declination in London? Explain how it varies if you travel due north from London. What is the general course of the agonic line? FREEHAND DRAWING. Time allowed, 1 hour. [No instruments of any kind allowed.] 1. Draw an oval having its longer diameter equal to 24 inches and its shorter to 1 inch. 2. Copy as accurately as you can the drawing placed before you. 3. Make a copy in any method you prefer of any portion of the photograph placed before you. GEOMETRICAL DRAWING. Time allowed, 1 hour. [The constructions must be neat and accurate, constructive lines being shown in dots. No written descriptions are necessary. All the work is to be inked in.] 1. Draw 9 circles of inch radius in three rows, their centres to be in lines parallel to each other and 1 inch apart. 2. Draw a circle with a radius of inch. Inscribe and circumscribe this circle with two equilateral triangles having their sides parallel. 3. Find a mean proportional between two lines 24 inches and inch long, and figure its length on the diagram. 4. Draw a regular hexagon of 1 inch side and within it six equal circles, each touching two other circles and also two sides of the polygon. 5. Draw a circle with a radius of 1 inch, and place in it a chord such that the angle standing on it and having the point in the circumference may be 47°. EXAMINATION FOR ADMISSION TO THE ROYAL MILITARY ACADEMY, WOOLWICH. MATHEMATICS. Time allowed, 3 hours. 1. If building ground be bought for 15s. 9d. a square yard, what will be the cost of half an acre of such ground? The purchaser of the half acre builds a house upon it and lays out the ground at a further cost of 20941. 5s., what rent per annum must he obtain so as to realize 9 per cent. on his whole outlay? 2. If 20 English navvies, each earning 3s. 6d. a day, can do the same piece of work in 15 days that it takes 28 foreign workmen, each earning three francs a day to complete in 20 days; taking the value of the franc at 10d., determine which class of workmen it is most profitable to employ. If a piece of work done by navvies cost 30007., what would be the cost of the same work done by foreign workmen? Divide 2.47. by 00625, and without using the common rule for the extraction of the square root, prove that 1.83 is the square root of 3.361. 4. What is meant by the "course of exchange" between two countries? A merchant in New York wishes to remit to London 5110 dollars, a dollar being equal to 4s. 6d. English, for what sum in English money must he draw his bill when bills on London are at a premium of 9 per cent.? 5. Investigate the rule for affixing the characteristics to the tabulated logarithms of numbers, whether they be whole numbers or decimals. Express log. 10 00001. Find by the aid of the tables (1.) (·004725). (3.) The number of years in which the amount of an annual sinking fund of five millions would pay off a national debt of 800 millions, allowing five per cent. compound interest. 6. Multiply (x3 + 2 a x2 + 3 a2 x + a3) by (x3 + 2a x2 3a2 x -- a3). 7. Prove (a)+(x-6)2 + (x−c)2 + 2 { (x − a) (x —b) = = 9x2-6x (a + b + c) + (a + b + c)2. Solve the equation x3 8x2+ 19 x it into one whose roots are each less by unity than the roots of the given equation. 4 9. When are numbers in harmonical progression? 2, 1, are three cong' secutive terms of a harmonical progression. What are the terms immediately preceding and following them? If three arithmetic means be inserted between (a) and (b), and three harmonic means between (b) and (a), prove that the product, of any two corresponding terms in each series is a b. 10. Assuming the form of the general term of the expansion of (1 + x)* when (n) is a positive integer, show that the coefficient of the (n)ch term reckoned from the beginning of the series is equal to the coefficient of the (n)th term reckoned from the end. Express the middle term of (x with a denominator (1.2.3...n), and find the greatest term in the expansion of 11. If (k) be the coefficient of (x) in the expansion of a*, prove = 1 1 1 + + &c. 3 (2n+1)3 &c.}. Given log.. 3 1.0986; obtain from the above series log.. 10, and show how log.. 10 connects the Napierian with the tabular logarithm of any number. 12. Express N as a continued fraction, where N is a whole number, not a perfect square. If (a) be the greatest integer in N, show that (2a) is the greatest quotient that will appear in the continued fraction. Find 18 in the form of a continued fraction, and point out the recurring period of the quotients. Time allowed, 3 hours. 1. Define parallel straight lines, and a parallelogram. The opposite sides of parallelograms are equal to one another. 2. When does a straight line touch a circle? The straight line drawn at right angles to the diameter of a circle from the extremity of it, touches the circle. 3. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and have those angles equal which are opposite to the homologous sides. Under what given circumstances does Euclid prove that two triangles will be similar? 4. When is a straight line at right angles to a plane, and when is one plane perpendicular to another? From the same point in a given plane there cannot be two straight lines at right angles to the plane upon the same side of it. 5. If ABCD be a quadrilateral figure inscribed in a circle, and if it is bisected by its diameter B D, prove that A B: BC= CD: DA. 6. Write down without proof the value of sin. 390°, tan. (-240°), cos. 495°. Assuming the expression for tan. (A + B) in terms of tan. A and tan. B, express tan. 3 A in terms of tan. À. If ABC be a triangle wherein C is a right angle, and if the straight line AD be drawn to meet BC in D, and to make the angle DAC to be a third part of the angle BAC, prove that CD is always less than a third part of C B. 7. What is meant by the circular measure of an angle? If is the circular measure of an angle which is one-third of a places of decimals. 9. Show why we may expect in a table of sines to find the "differences" greatest at the beginning and growing less as the table proceeds. 10. A B, AC, are two straight lines, including the angle 45. B is a point whose distance from A is known to be 1000 yards. An observer moves from A along A C until at a point P in A C he finds the angle BPA to be 127 19'. What is the distance of P from A? 11. When a triangle A B C is solved from the given parts A B 100 feet, BC 56 feet, the angle B A C = 27° 18′ 54′′, find the difference of the two values obtained for the angle B. = 12. Express the radius of the circle inscribed in a given triangle in terms |